Abstract
The estimation of fixed effects is considered for small, unbalanced, mixed linear models. The two-stage estimator, in which the variance components are first estimated by ML or REML, is compared to the intra-block (IB) estimator, the ordinary least squares (OLS) estimator (ignoring the random effects) and the Gauss-Markov (GM) estimator. Comparison is made, based on 100 simulated data sets each, for 6 designs (3 BIBD's and 3 unbalanced designs). In comparing loss of information, relative to the GM lower bound, the two-stage procedures (using either ML or REML) are recommended for all but the smallest and least balanced design. The study also compared estimates of the variance of the two-stage estimators, using either the GM lower bound or the Kackar-Harville (KH) approximation. Estimators of the variance using REML estimates of the variance components are recommended, since estimators using ML estimates were seriously biased downward for all designs considered.
Keywords
Mixed model, variance components, REML, ML, twostage estimator, recovery of inter-block information, Kackar-Harville variance approximation.
Creative Commons License
This work is licensed under a Creative Commons Attribution-Noncommercial-No Derivative Works 4.0 License.
Recommended Citation
Nabugoomu, F. and Allen, O. B.
(1993).
"THE ESTIMATION OF FIXED EFFECTS IN A MIXED LINEAR MODEL,"
Conference on Applied Statistics in Agriculture.
https://doi.org/10.4148/2475-7772.1376
THE ESTIMATION OF FIXED EFFECTS IN A MIXED LINEAR MODEL
The estimation of fixed effects is considered for small, unbalanced, mixed linear models. The two-stage estimator, in which the variance components are first estimated by ML or REML, is compared to the intra-block (IB) estimator, the ordinary least squares (OLS) estimator (ignoring the random effects) and the Gauss-Markov (GM) estimator. Comparison is made, based on 100 simulated data sets each, for 6 designs (3 BIBD's and 3 unbalanced designs). In comparing loss of information, relative to the GM lower bound, the two-stage procedures (using either ML or REML) are recommended for all but the smallest and least balanced design. The study also compared estimates of the variance of the two-stage estimators, using either the GM lower bound or the Kackar-Harville (KH) approximation. Estimators of the variance using REML estimates of the variance components are recommended, since estimators using ML estimates were seriously biased downward for all designs considered.
